EFFECT OF A SHEAR-FLOW ON THE PLANFORM OF THERMAL-CONVECTION IN A FLUID OF VARIABLE VISCOSITY

It is well known that if the variation with temperature of viscosity is taken into account, the onset of convection in an infinite layer of fluid that is heated from below takes the form of hexagonal convection cells. It is also well known that in a sufficiently strong shear flow, rolls aligned with the flow direction are the preferred mode of convection. Here the process by which a steady or unsteady shear flow destroys the usual hexagonal cell pattern is investigated. The critical size of the shear dow that enables rolls to be established at the onset of convection is determined for the case when the stress is prescribed at the boundaries.